By Hans-Peter Blatt (auth.), Robert Schaback, Karl Scherer (eds.)
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Additional resources for Approximation Theory: Proceedings of an International Colloquium Held at Bonn, Germany, June 8–11, 1976
13) follows at once from the lemma. The second assertion of the corollary is less obvious. For its proof, assume without loss that ~ = O. 13), 45 0 < •i-la E a~, i=1,2,3, -i<~
Weiss, TU Wien, for interesting d i s c u s s i o n s about this paper, P. -Math. TU K a r l s r u h e , f o r his help in p r o g r a m m i n g the examples and to Mrs. M. Zahn for typing the manuscript. : Ober die Mittelwerteigenschaft auf die Newton'schen Bericht Nr. 75/4 des Instituts Brakhase, 183-196 25, 409-419 Mathematik, E gx~ L. T. Num. Math. Rep. Nr° 14/75, Technische GoodwSn: Some new methods Pereyra, for numerical equations, Proc. to the limit in the solution of ordinary differential equations, UCLA (1963).
Konvexen Approximationsproblems bestimmen. F~r jede zugeordnete Kurve gilt dann die Absch~tzung: ILf-g~il~ilf-g-~hli +iigk-g-~hEl ~il(I-~) (f-g)II+xflf-g-hii+ o (~) (2) f~r hinreichend kleine ~. Also existiert in j eder Umgebung eine bessere Approximation. Mit dem Beweis ist das allgemeine Schema fOr die Verfahren vom NewtonTyp vorgezeichnet. $6 Alg0rithmns. O. W~hle einen Startwert go" Setze v=O. I. Bestim~e zu g~ einen Tangentenvektor h=hv~CgG mit llf-g-hll
Approximation Theory: Proceedings of an International Colloquium Held at Bonn, Germany, June 8–11, 1976 by Hans-Peter Blatt (auth.), Robert Schaback, Karl Scherer (eds.)